Hall's Random Walk is based on a questionable assumption and Flavin's imprecision on the mathematical summation of future incomes)

Hall (1978) wrote a very short proof of his random walk result in the appendix. Flavin (1981) wrote in the same Journal of Political Economy a step by step microfoundation approach to change in consumption with an imprecise summation of future incomes for period t+1. Under Clower's Dual-Decision Hypothesis, we will show why Hall's Permanent Income Hypothesis assumption is questionable and impractical. Here is Flavin's approach and how she arrived at Hall's result:

Why Flavin's consumption at period t+1 is incorrect